The most ignored and unpopular section of GRE among students can be a bane to your application if you choose not to prepare for it well. I have myself seen cases, where good students with good GRE scores (320+) fail the admission process due to low AWA scores (less than 4). The reason which puts off Professors and university recruiters when they see AWA scores regardless of is twofold:

• Lack of Verbal ability (conclusion derived from your AWA scores and low verbal scores... your actual verbal ability may be quite good) will make your chance of integrating with society and getting VISA becomes harder.
• Without good grasp on the language the recruiters don't trust you to help them with teaching activities and research writing works which puts you in a big disadvantageous position already.

What is a good AWA score then

This brings us to the next part of this post, What is a good AWA score then? In my experience, any score greater than equal to 4.5 is good and any score less than 4 is disastrous. A score of 4 in AWA is not bad either, however good scores in verbal and quants section can compensate for it. This leads to our next part of this post, how can you judge your own writing and how ETS judges your writing. I am not going to suggest 5 tips to improve your writing score, because you will find tons of posts suggesting those.
I won't join the herd, instead I will just delineate the merits GRE looks for in your essays and assign a score according to those.

Score Level Descriptions for the Analytical Writing Measure

Although the GRE® Analytical Writing measure contains two discrete analytical writing tasks, a single combined score is reported because it is more reliable than a score for either task alone. The reported score ranges from 0 to 6, in half-point increments.
The statements below describe, for each score level, the overall quality of analytical writing demonstrated across both the Issue and Argument tasks. The test assesses "analytical writing," so critical thinking skills (the ability to reason, assemble evidence to develop a position and communicate complex ideas) are assessed along with the writer's control of grammar and the mechanics of writing (e.g., spelling).

Scores 6 and 5.5

Sustains insightful, in-depth analysis of complex ideas; develops and supports main points with logically compelling reasons and/or highly persuasive examples; is well focused and well organized; skillfully uses sentence variety and precise vocabulary to convey meaning effectively; demonstrates superior facility with sentence structure and language usage, but may have minor errors that do not interfere with meaning.

Scores 5 and 4.5

Provides generally thoughtful analysis of complex ideas; develops and supports main points with logically sound reasons and/or well-chosen examples; is generally focused and well organized; uses sentence variety and vocabulary to convey meaning clearly; demonstrates good control of sentence structure and language usage, but may have minor errors that do not interfere with meaning.

Scores 4 and 3.5

Provides competent analysis of ideas; develops and supports main points with relevant reasons and/or examples; is adequately organized; conveys meaning with reasonable clarity; demonstrates satisfactory control of sentence structure and language usage, but may have some errors that affect clarity.

Scores 3 and 2.5

Displays some competence in analytical writing, although the writing is flawed in at least one of the following ways: limited analysis or development; weak organization; weak control of sentence structure or language usage, with errors that often result in vagueness or lack of clarity.

Scores 2 and 1.5

Displays serious weaknesses in analytical writing. The writing is seriously flawed in at least one of the following ways: serious lack of analysis or development; lack of organization; serious and frequent problems in sentence structure or language usage, with errors that obscure meaning.

Scores 1 and 0.5

Displays fundamental deficiencies in analytical writing. The writing is fundamentally flawed in at least one of the following ways: content that is extremely confusing or mostly irrelevant to the assigned tasks; little or no development; severe and pervasive errors that result in incoherence.

Score Level 0

The examinee's analytical writing skills cannot be evaluated because the responses do not address any part of the assigned tasks, are merely attempts to copy the assignments, are in a foreign language or display only indecipherable text.

Therefore, its a good way to assess your own writing before you dive into preparation of AWA. Knowing your strengths and weaknesses is 50% of the preparation itself. So good luck!
PS: ETS has a software called ScoreItNow which will evaluate your AWA essasys. Follow this link